Exceptional Legendre polynomials and confluent Darboux transformations

• Verfasst von: García-Ferrero, María Ángeles [VerfasserIn]
• Verfasst von: Gómez-Ullate, David [VerfasserIn]
• Verfasst von: Milson, Robert [VerfasserIn]
• Titel: Exceptional Legendre polynomials and confluent Darboux transformations
• Verf.angabe: María Ángeles García-Ferrero, David Gómez-Ullate and Robert Milson
• E-Jahr: 2021
• Jahr: February 20, 2021
• Umfang: 19 S.
• Teil: volume:17
• Teil: year:2021
• Teil: elocationid:016
• Teil: pages:1-19
• Teil: extent:19
• Fussnoten: Gesehen am 29.06.2021
• Titel Quelle: Enthalten in: Symmetry, integrability and geometry: methods and applications
• Ort Quelle: [S.l.], 2005
• Jahr Quelle: 2021
• Band/Heft Quelle: 17(2021), Artikel-ID 016, Seite 1-19
• ISSN Quelle: 1815-0659
• DOI: doi:10.3842/SIGMA.2021.016
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1761470922

Abstract

Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of Hermite, Laguerre, and Jacobi polynomials by allowing for polynomial sequences that miss a finite number of ''exceptional'' degrees. In this paper we introduce a new construction of multi-parameter exceptional Legendre polynomials by considering the isospectral deformation of the classical Legendre operator.